Question

[chu ngọc trâm anh]

CMR

a) \(\left(x-3\right)\left(x-5\right)+4>0\)

b)\(a^2+a+1>0\)

c)\(a^2-a+1>0\)

Answer 1

[Kiệt Nguyễn]

b) Ta có: \(a^2+a+1=a^2+2.\frac{1}{2}a+\frac{1}{4}+\frac{3}{4}\)

\(=\left(a+\frac{1}{2}\right)^2+\frac{3}{4}>0\forall a\)

Vậy \(a^2+a+1>0\left(đpcm\right)\)

Answer 2

[Incursion_03]

\(a,\left(x-3\right)\left(x-5\right)+4=x^2-8x+15+4=\left(x-4\right)^2+3>0\)

\(b,a^2+a+1=\left(a+\frac{1}{2}\right)^2+\frac{3}{4}>0\)

\(c,a^2-a+1=\left(a-\frac{1}{2}\right)^2+\frac{3}{4}>0\)